Select the coordinates A′

Question

and B′
after dilation of the line segment AB
with a scale factor of 13
, centered at the origin where the endpoints are A(−6,3)
and B(−12,9)
.(1 point)
Responses

A′(−2,1)
and B′(−12,9)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 12 comma 9 right parenthesis

A′(−2,1)
and B′(−4,3)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(−6,3)
and B′(−4,3)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(−18,9)
and B′(−36,27)

Answer 1

To find the coordinates of points A' and B' after dilation of the line segment AB with a scale factor of 13, centered at the origin, we use the formula for dilation:

\[ (x', y') = (k \cdot x, k \cdot y) \]

where \(k\) is the scale factor, and \((x, y)\) are the original coordinates.

Given:

• Point A \((-6, 3)\)
• Point B \((-12, 9)\)
• Scale factor \(k = 13\)

Now, we can apply the dilation to each point:

1. For point A: \[ A' = (13 \cdot (-6), 13 \cdot 3) = (-78, 39) \]

2. For point B: \[ B' = (13 \cdot (-12), 13 \cdot 9) = (-156, 117) \]

Now, let's check the provided options:

• A′(−2,1) and B′(−12,9)
• A′(−2,1) and B′(−4,3)
• A′(−6,3) and B′(−4,3)
• A′(−18,9) and B′(−36,27)

None of these options matches the dilated points (-78, 39) and (-156, 117).

It seems there may be an issue as none of the provided responses is correct based on the calculation for the specified dilation. The coordinates after dilation should be A'(-78, 39) and B'(-156, 117).